条形非线性椭圆方程稳定解的不存在性研究

IF 1.6 3区数学 Q1 MATHEMATICS

Analysis and Mathematical Physics Pub Date : 2025-07-17 DOI:10.1007/s13324-025-01107-0

Cherif Zaidi

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引用次数: 0

摘要

本文研究了一类非线性椭圆方程解的不存在性，重点讨论了稳定或稳定在紧集外、潜在无界和变符号的解。我们的主要方法包括积分估计、pohozaev型恒等式和单调性公式。我们的分类方法是一个明显的结果，特别是在次临界情况下（即\(1< p < \frac{n+4}{n-4}\)），我们在\(H^2 \cap H_0^1(\Omega )\)的子空间中建立了一个具有莫尔斯指数为1的山口解的存在性，该解表现出圆柱对称。

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A study on the nonexistence of stable solutions for nonlinear elliptic equations in strips

In this paper, we investigate the nonexistence of solutions of certain nonlinear elliptic equations, focusing on solutions that are stable or stable outside a compact set, potentially unbounded, and sign-changing. Our primary methods include integral estimates, Pohozaev-type identity and the monotonicity formula. Our classification approaches as a sharp result, specifically, in the subcritical case (i.e, \(1< p < \frac{n+4}{n-4}\)), we establish the existence of a mountain pass solution with a Morse index of 1 in the subspace of \(H^2 \cap H_0^1(\Omega )\) that exhibits cylindrical symmetry.

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来源期刊

Analysis and Mathematical Physics MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.70

自引率

0.00%

发文量

122

期刊介绍： Analysis and Mathematical Physics (AMP) publishes current research results as well as selected high-quality survey articles in real, complex, harmonic; and geometric analysis originating and or having applications in mathematical physics. The journal promotes dialog among specialists in these areas.